1Ellen L. Walker ImageJ Java image processing tool from NIH Reads / writes a large variety of images Many image processing operations are implemented Good rapid prototyping / testing tool Includes the ability to write your own plugins Convenient way to implement your own algorithms, using their image class and i/o methods

2Ellen L. Walker Point Processes Pixel by pixel transformation Output pixel depends only on corresponding input pixel Examples: Out(r,c) = In(r,c) * 1.25 Out(r,c) = In(r,c) + 25 Out(r,c) = (In(r,c)) 2

3Ellen L. Walker Linear Transformations Out(r,c) = In(r,c) * gain + bias Gain controls contrast Bias controls brightness Location dependent: Out(r,c) = In(r,c) * gain(r,c) + bias(r,c) E.g. “sky darkening filter” Linear Blend Out(r,c) = (lambda) * In1(r,c) + (1-lambda) * In2(r,c) If In1 and In2 are images, a sequence of these from lambda = 0 to lambda=1 is an image dissolve

4Ellen L. Walker Histogram An image histogram counts the number of pixels at each brightness. Color images have 3 histograms (red, green, blue)

5Ellen L. Walker Information in Histogram Contrast (variation in brightness) Are bars spread over the whole range? Foreground vs. background color Are there two separate “peaks” with a valley between?

6Ellen L. Walker Applications of Histogram Thresholding Find a value that separates foreground / background values Look for a “valley” between two peaks (may or may not be what you need) Contrast enhancement Histogram equalization – spread the data as evenly through the histogram as possible Goal: wide, flat histogram

7Ellen L. Walker Example: Histogram Equalization Original Modified

8Ellen L. Walker Algorithm: Histogram Equalization Find cumulative distribution For each intensity I, c(I) = # pixels <= I Code: C[0]=Hist[0]; For(greylevel =1; greylevel < max; greylevel++){ C[greylevel] = Hist[greylevel] + C[greylevel-1]; C[greylevel] = C[greylevel] / (double)(rows*cols); }

9Ellen L. Walker Algorithm: Histogram Equalization Use C(I) as a lookup table to determine the final value of each pixel. Since C(I) ranges from 0 to 1 (why?), multiply C(I) by the max pixel value to get the output value Code: For(r=0;r<rows;r++) for(c=0;c<cols;c++) out[r][c] = C[(in[r][c])]*MAX;

10Ellen L. Walker Locally Adaptive Histogram Equalization Instead of doing histogram equalization using the whole image, compute the distribution for a moving window around the given pixel. Avoids effect of bright light at one corner washing out everything in the image.

11Ellen L. Walker Image Neighborhoods Neighborhoods can be defined for each pixel The two most common neighborhoods 4-neighborhood 8-neighborhood N WE S

12Ellen L. Walker Applying a Mask Mask is a set of relative pixel positions. One is designated the origin (0,0) - usually at center Each mask element is weighted To apply the mask, put the origin pixel over the image pixel and multiply weights by the pixels under them, then add up all the values. Usually this is repeated for every pixel in the image. Assumptions must be made for pixels near the edge of the image.

13Ellen L. Walker Mask application example Mask = Apply to every pixel in image: Result is Boundary pixels are gray

14Ellen L. Walker Mathematical Representation of Mask Operations Equation from Chapter 3 g is the output image f is the input image h is the mask (also called kernel) Short form (convolution operator)

15Ellen L. Walker Masks that "blur" "Box mask" - every pixel gets the average of its neighborhood 1 1 1After computing, divide by 9 (mask sum) 1 1 1to keep image from getting too bright "Weighted average" - divide by 16 after application

16Ellen L. Walker Why blur? Avoid effects of small random noise (“salt and pepper”) Remove small features to emphasize larger ones Bigger masks blur more / remove larger features Sequence of masks generates sequence of increasingly blurred images (useful for some matching algorithms) First step in sharpening the image (!) Sharp(x,y) = orig(x,y) + gamma (orig(x,y) – (blur * orig(x,y)))

17Ellen L. Walker Boundary Effects (padding) Figure 3.12

18Ellen L. Walker Common Masks Figure 3.13

19Ellen L. Walker Median Filtering Example of a non-linear filter Replace the central pixel of a window with the median pixel of the window Compare to box filter, which replaces with average value in the window Tends to preserve edges (why?)